Don't try and parse the term literally, the term is a contradiction - there's no such thing as an "illiberal democracy" for the reasons you specify. People who

Don't try and parse the term literally, the term is a contradiction - there's no such thing as an "illiberal democracy" for the reasons you specify. People who use that word simply mean "democracies where my personal views on things like immigration don't win". The term illiberal democracy is an especially empty one because more or less any decision can be phrased in terms of positive liberties - e.g. "restrictions on immigration preserve the liberty of voters to enjoy and propagate their own culture".